I'm confused; what would it mean for that statement to be false? It sounds equivalent to "If everything non-genetic that can raise intelligence is present and everything non-genetic that can lower intelligence is absent, then the part that's left, the non-non-genetic component, is 100% genetic."
You're correct, but you're missing his point. The point is that genes do determine maximum intelligence---certain people simply cannot be as smart as certain other people, regardless of how good their environment is to them.
I think you're missing pjscott's point. Sure, a fixed set of genes determines the maximum intelligence across varying environments, but it's equally true that a fixed environment determines the maximum intelligence across varying genes. How is one or the other "the" maximum?
You can measure and modify the environment for a growing child/youth with relative ease; but you cannot modify genetic makeup at all (for now). This makes the distinction a valuable one.
Think of a car analogy: Genetics is the engine's size and type, environment is the fuel/tyres/lubricant that were added. Quite possible to get very bad performance out of a car with no engine oil or fuelled with diesel instead of petrol - but once these "hygiene factors" are addressed, the maximum performance is determined by innate factors.
People who shoot down science because it's racist/sexist/etc. are shooting down the truth. People who make overreaching claims are just as detrimental. I think intelligence is very largely genetic. Claiming its "purely genetic" only gives more fodder for the "that's racist"-types to shoot it down.